#This shows that component groups can behave strangely under isogenies
# Spin(3,1)=SL(2,C) is connected
# SO(3,1) is not connected
# PS(3,1)=PSL(2,C) is connected
#
#Note that SO(3,1) is not a complex group (!)
This is the Atlas of Reductive Lie Groups Software Package version 0.2.3.
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empty: type
Lie type: A1.A1
elements of finite order in the center of the simply connected group:
Z/2.Z/2
enter kernel generators, one per line
(ad for adjoint, ? to abort):
sc
enter inner class(es): C
main: components
there is a unique real form: sl(2,C)
group is connected
real: type
Lie type: A1.A1
elements of finite order in the center of the simply connected group:
Z/2.Z/2
enter kernel generators, one per line
(ad for adjoint, ? to abort):
1/2,1/2
enter inner class(es): s
too few inner class symbols
enter inner class(es) (? to abort): s s
main: components
(weak) real forms are:
0: su(2).su(2)
1: sl(2,R).su(2)
2: su(2).sl(2,R)
3: sl(2,R).sl(2,R)
enter your choice: 3
component group is (Z/2)^1
real: type
Lie type: A1.A1
elements of finite order in the center of the simply connected group:
Z/2.Z/2
enter kernel generators, one per line
(ad for adjoint, ? to abort):
ad
enter inner class(es): C
main: components
there is a unique real form: sl(2,C)
group is connected